In this technical note, we present a Receding Horizon Control (RHC) design method for linear parameter varying (LPV) systems subject to input and/or state constraints based on a class of nonlinearly parameterized Lyapunov functions recently introduced by Guerra and Vermeiren. As it will be made clear, their use gives rise to less conservative stabilizability conditions w.r.t. those arising from quadratic Lyapunov functions. A workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state-feedback control laws complying with the prescribed constraints. This control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed. Numerical comparisons with existing RHC methods for LPV systems are reported in the final example.